基于F-P标准具的微小角度测量装置的误差建模与修正
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中国计量大学计量测试与仪器学院杭州310018

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TH71

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国家自然科学基金(52475577,51875543)项目资助


Error modeling and correction of a small-angle measurement device based on F-P standard etalon
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College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou 310018, China

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    摘要:

    测角仪器或装置中,反射镜和转台对测角精度具有不可避免且往往是主导性的影响。为深入揭示这些因素在基于F-P标准具的测角系统中所引入的系统性偏差,系统建立了反射镜与转台造成的微小角度测量误差数学模型,并在此基础上展开综合分析与误差修正研究。模型严格考虑反射镜俯仰角误差、初始零位角误差、偏心误差以及转台安装误差和转轴偏心误差多种误差源,结合矩阵运算、矢量描述和三维坐标变换方法,推导不同误差作用下干涉圆环圆心在成像面上发生的位移规律,从而构建能够完整反映系统误差传播路径的理论框架。进一步利用MATLAB软件对上述误差对微小角度测量结果的影响程度进行定量分析,并分别研究误差源之间不存在耦合与存在耦合两种情形下的误差主导性。结果显示,当忽略误差耦合时,反射镜偏心误差对微小角度测量精度影响最为显著;而在考虑误差之间可能存在的耦合关系后,通过主成分分析(PCA)方法提取主要影响成分,可见反射镜偏心误差与初始零位角误差共同成为影响微小角度测量的主要因素。依据分析结论,对反射镜偏心误差进行针对性修正,在测量范围为1 800″时,测量精度由±1.93%FS显著提升至±0.22%FS,微小角度测量误差整体降低达91.9%,验证了模型与修正方法的有效性。

    Abstract:

    In angle-measurement instruments,the mirror and rotary stage inevitably influence and often determine measurement accuracy.To clarify the systematic deviations introduced in the F-P etalon-based angle-measurement system,this article formulates a mathematical model describing micro-angle measurement errors caused by the mirror and the rotary stage,followed by a comprehensive analysis and correction.The model incorporates mirror pitch-angle error,initial zero-position angle error, eccentricity error,rotary-stage installation error, and rotation-axis eccentricity error.Through matrix operations and three-dimensional coordinate transformations, the displacement of the interference-ring center on the imaging plane under various errors is derived, forming a complete error-propagation framework. MATLAB is used to quantify the influence of each error source,examining cases with and without coupling.Results show that without coupling, the mirror eccentricity error dominates, whereas with coupling, principal component analysis (PCA) indicates that the mirror eccentricity error and initial zero-position angle error jointly exert the greatest impact. Based on this analysis, a targeted correction for mirror eccentricity is implemented. Within a measurement range of 1 800″, accuracy improves from ±1.93%FS to ±0.22%FS,reducing micro-angle measurement error by 91.9%. The effectiveness of the model and correction strategy is evaluated.

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李泽林,沈小燕,李蕾,刘畅,杨昊泽.基于F-P标准具的微小角度测量装置的误差建模与修正[J].仪器仪表学报,2025,46(12):154-163

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  • 在线发布日期: 2026-03-02
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